Base mesh is rendered differently between viewport and final render with animation
I tested it with Blender 2.79 and it works well. As you could see on the image below the possible problem could be the inactive Armature Modifier for the render circled in red.



On the other hand, I opened Your .blend file, load my custom HDRI map to light-up the scene, just render and everything is matching for me (even with that modifier turned off) as you could also check on the picture. Does this helps?

Sincerely, Jan